System and method for inverse multilateration

ABSTRACT

A method and system for location-determination of a mobile comprising of a receiver with a variable processor gain of up to 45.15 dB for detecting signals transmitted from transmitters that at a farther distance as well as from transmitters that are situated in sparsely populated areas. The system also includes a plurality of terrestrially deployed transmitters known as “pseudolites” that broadcast GPS-like signals, and in addition implementing the use of existing, available information from modulated signals, such as phase, amplitude and convolution with pseudorandom codes.

FIELD OF THE INVENTION

A system and method for determining location by using modulated signals,including code division multiple access (CDMA) and time divisionmultiple access (TDMA) wireless communication signals, to complement orreplace global positioning system (GPS) signals is disclosed. Inparticular, a system and method for exploiting inverse multilaterationtechniques to locate communication transceivers is disclosed.

BACKGROUND OF THE INVENTION

The ability to accurately determine one's location has long been asought after goal. To that end, location determining systems have beendeveloped. For example, GPS and other systems can be used to determinelocation.

One drawback associated with GPS is that, in some locations, receptionof the required satellite signals is poor. Furthermore, GPS requiresrelatively expensive satellites and precision timing (usually withatomic clocks).

Other drawbacks of GPS systems are that they can experience geometricdilution of precision (GDOP). For example, GDOP can arise from errorspropagated through the satellite signal transmission and throughround-off errors in calculation.

In addition, the process of searching for and acquiring GPS signals,reading the ephemeris data for a multiplicity of satellites andcomputing the location of the receiver from this data can be timeconsuming, often requiring several minutes. In many cases, this lengthyprocessing time may render the information unusable.

On the other hand, in existing cellular systems a mobile telephone'slocation within the cellular system can be estimated by measuring a thetime difference of arrival (TDOA) of signals transmitted to or from themobile unit. TDOA depends on a number of factors some of which include,the number of receiving locations, the number of diverse antennas ateach cell site, the average distance from the transmitting unit to eachof the receiving base stations, the average height of the receivingantennas, and the average antenna power gain in the direction of thetransmitting unit. Some TDOA systems may require a large number ofwell-placed sensors in order to get a robust, enhanced accuracymeasurement. Hence, there is a need for fast, relatively inexpensive,yet accurate method of determining the location of an object.

Another drawback of existing systems is that it is that the location ofcommunication transceivers is not always accurately known. Some existingmultilateration techniques rely on computations for which the knownpositions of transceivers is critical. Other drawbacks also exist.

SUMMARY OF THE INVENTION

Some embodiments of the present invention utilize apparatus thatcomprises a stand-alone receiver capable of at least a 40-45.15 dBprocessing gain (based on the short code length of 32,768). In someembodiments, the receiver may receive and digest CDMA timinginformation, and use it in a GPS-like computation to determine thereceiver location.

In another embodiment of the present invention, there is provided asystem and method, based on CDMA cellular radio standard signals. TheCDMA signals may be used to provide timing data to enable positioncomputations.

For example, in some embodiments, each cell site may transmit asynchronous signal that is correlated with GPS signals (which typicallyhas a Rubidium or other atomic standard clock backup). Because of suchsynchronization, a Pilot signal from each cellular base station can bedemodulated and, thereby, yield an accurate time of arrival (TOA) for asignal to a receiver. When there are multiple base stations (e.g., threebase stations), transmitting to a receiver then the position of thereceiver can be determined by triangulation, multilateration or otherposition computation technique.

One advantage of some embodiments of the invention is that they can beimplemented using the existing cellular infrastructure. Typically, thisinfrastructure includes thousands of transmitters across the UnitedStates and other countries, many of which contain battery backup powersystems, and employ numerous support personnel. In addition, at leasttwo separate entities exist that transmit their signals at differentfrequencies (800 MHz and 1.9 GHz). For at least these reasons, aformidable, robust and relatively inexpensive infrastructure exists toprovide a backup or supplemental pseudo-GPS system in accordance withembodiments of the invention.

In accordance with some other embodiments of the invention there isprovided a system for determining the position of an object by inversemultilateration techniques. In these embodiments a mobile detectionsystem (e.g., handheld, vehicle mounted, aircraft mounted, watercraftmounted, etc.) may be enabled to determine its own location as it moves.

Other advantages and features of the invention also exist. The followingdescription sets forth some advantages and features of some embodimentsof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The purpose and advantages of the present invention will be apparent tothose of ordinary skill in the art from the following detaileddescription in conjunction with the appended drawings in which likereference characters are used to indicate like elements.

FIG. 1 is a schematic block diagram of a receiver according toembodiments of the invention.

FIG. 2 is a flow chart of a receiver location technique according toembodiments of the invention.

FIG. 3 is an illustration of a system and method to determine thelocation of a receiver according to embodiments of the invention.

FIG. 4 is an illustration of a system for determining the location of anobject in the absence of GPS satellites and in the event that a requirednumber of cellular base stations are not available according to someembodiments of the invention.

FIG. 5 is an illustration of a system and method for implementinginverse multilateration techniques to determine the location oftransceivers in a mobile position detection system according to someembodiments of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

The following description is intended to convey a thorough understandingof the invention by providing a number of specific embodiments anddetails involving the structure and operation of a novel apparatus. Itshould be understood, however, that the invention is not limited tothese specific embodiments and details, which are provided for exemplarypurposes only. It should be further understood that one possessingordinary skill in the art, in light of known apparatuses and methods,would appreciate the use of the invention for its intended purposes andbenefits in any number of alternative embodiments, depending uponspecific design and other needs.

FIG. 1, is an schematic illustration of a circuit for a receiverapparatus of 200 in accordance with some embodiments of the invention.Receiver 200 may receive a signal (e.g., a CDMA pilot pseudo noise (PN)signal) from a transmitter via antenna 205. The signal may be amplified(e.g., using a low noise amplifier 210). Receiver 200 may also includein-phase mixer 215, quadrature mixer 220 and an oscillator circuit 230for down converting the CDMA signal from the CDMA frequency to a lowerfrequency and then digitizing the lower frequency GPS signal into anin-phase I and quadrature phase Q digital signals. Receiver 200 may alsoinclude a variable length pseudorandom generator 265 to generate a codeof suitable length. For example, some embodiments may generate a codelength of 128-32,768 bits.

The in-phase portion (I) of the signal may be fed into a early 235, true245, and late 255 correlators. Similarly, the quadrature phase (Q)portion of the signal may be fed into an early 240, true 250, and late260 correlators.

In some embodiments, a stored reference of the variable length generatormay be defined by the pilot PN sequence based on the followingcharacteristic polynomials:PI(x)=x ¹⁵ +x ¹³ +x ⁹ +x ⁸ +x ⁷ +x ⁵+1

-   -   (for the in-phase (I) sequence)        and        PQ(x)=x ¹⁵ +x ¹² +x ¹¹ +x ¹⁰ +x ⁶ +x ⁵ +x ⁴ +x ³+1    -   (for the quadrature (Q) phase sequence).

These orthogonal codes are taken from the any suitable specifications(e.g., the IS-95 specification) and can be modified for othercommunication system in the future.

The outputs 237, 242, 247, 252, 257 and 262 are passed onto a logiccontrol and processing block 270, in order for the signal to beprocessed.

In some embodiments, an increase in accuracy, may be obtained byoversampling the base band signals by a factor of 100 (e.g., 122.55MHz). Doing so may increase the precision of the systems measurement oftime of arrival of such signals to approximately 2.44 meters (e.g., asdetermined from (3×10⁸ meters/sec)/(122.55 MHz). The amount ofoversampling may be increased as the speed of available digitalelectronic circuits increases. Increased oversampling may be implementedto obtain greater precision in determining the location of the receiver.

Precision of the location determination may also be increased by othermechanisms. For example, precision will also increase as the chipfrequency increases. It is anticipated that the WCDMA system planned forimplementation in Europe within the next five years will have a chiprate of 3.84 MHz and the IS-2000 system which is in use today in theUnited States has provisions for a chip rate of at least 3.6864 MHz.

In some embodiments, it may be desirable to determine accurate locationsfor the antennas transmitting the timing signals (in CDMA thetransmission antennas may be differentiated by assigned PN offsets). Ingeneral, this determination may be accomplished by obtaining a sample oftransmitting antennas in a given survey area (e.g., about 10 antennasfor every 1000 square miles) and then utilize location data (e.g., asprovided by GPS) along with data collected from a suitable receiver(e.g., receiver 200) to determine transmitting antenna locations.

FIG. 2 is a flow diagram illustrating a method for determiningtransmitting antenna location for some embodiments of the invention.Determining the location of a transmitting antenna may begin, asindicated at 310, with a survey of the area for which the transmittingantennas are to be located. The survey may be accomplished in anysuitable manner (e.g., satellite imaging, GPS data, aerial survey orsome other suitable technique). A suitable variable gain receiver (e.g.,receiver 200) may be used to detect PN offset correlated with each basestation antenna in the survey area. Preferably, the location of thereceiver (e.g., receiver 200) may be accurately determined (e.g., fromTDOA data or GPS data or some other reasonably accurate location system)as indicated at 315.

In embodiments where the survey is being performed from an aerialplatform, it may be preferable for the aerial platform to circle orotherwise traverse the region of interest. For example, the aerialplatform may circle and change elevation as indicated at 320. Thistraversal of the region of interest is performed in order to obtain dataon the exact position of the transmitting object. It is preferable toobtain position data for each relevant dimension, therefore, the mobiledetection platform may traverse the x, y and z planes. In an airplane(or other aerial device) one way to accomplish this traversal is to flythe airplane up in a spiral motion. In embodiments with other types ofmobile platforms (e.g., land based or water based) similar traversalsmay be performed to collect data on the relative position of thetransmitting object in reference to the detecting platform on allrelevant position dimensions (e.g., x, y, and z axes).

Once this data is collected, the position of the base stationtransmitting antenna may be determined with an appropriate calculationas indicated at 325. For example, an inverse multilateration calculationmay be performed in some embodiments.

As indicated at 330, the process of locating base station antennas maycontinue as desired. In addition, the locations of base station antennasmay preferably be stored in a database or other retrievable system tofacilitate actual operation of the systems and methods described herein.

In embodiments of the invention where the locations of base stationantenna transmitters have been located (e.g., as described above inconnection with FIG. 2) or are otherwise known, a variable gain receiver(e.g., receiver 200) may be used as a location determining device in thefollowing manner. As shown in FIG. 3, system may comprise any number ofmodulated signal transmitter base stations (e.g., three base stations410(a)-410(c) are shown in FIG. 4). The modulated signal may betransmitted in any suitable frequency range. For example, the basestations 410(a)-410(c) may be part of a CDMA or other cellularradio-frequency system.

A suitable receiver 420 (e.g., a variable gain receiver 200 with asuitable amount of gain as described in connection with FIG. 1) may beused to determine the location of the receiver within the system 400.The receiver 420 may comprise a hand-held device, a vehicle, aircraft orwatercraft mounted device, and may be integrated into another device(e.g., a cellular phone, laptop or palm top computer, or the like).

During operation of some embodiments, the modulated signals (e.g., CDMAcellular radio standard signals) are used to provide data, part of whichis an accurate timing signal, that, together with the known base stationlocations, can be used to determine receiver 420 location. For example,each of base stations 410(a), 410(b) and 410(c) may broadcasts a pilotsignal synchronized among the base stations. Receiver 420 demodulateseach pilot signal, thereby triangulating the position of the receiverbased on the time difference of arrival (TDOA) of the pilot signals fromeach base station and to determine the location of the receiver from theknown locations of the base stations 410(a)-410(c). Techniques fordetermining receiver location, such as triangulation, TDOA, time ofarrival (TOA), multilateration and the like are known and any suitabledetermination may be used in accordance with embodiments of theinvention.

In some embodiments of the invention, the variable gain receiver (e.g.,receiver 200) may be used as a backup or supplement to an existinglocation determining system. For example, another embodiment shown inreference to FIG. 4, illustrates a system for determining the locationof an object in the absence of GPS satellites and in the event that arequired number of cellular base stations are not available. System 500,may utilize CDMA signals in conjunction with ground-based transmittersknown as pseudolites (or pseudo satellites) that broadcast GPS-likesignals from terrestrial locations. An entity, such as an aircraft 515(or a vehicle, watercraft, handheld receiver, etc.), typically employs aGPS satellite navigation system (e.g., including signals transmittedfrom GPS satellites 510 with only one satellite shown for ease ofillustration) in order to determine its position coordinates. In theevent of the loss of GPS signals due to the lack of line of sight or anyother such factors, aircraft 515, which may comprise a variable gainreceiver (e.g., receiver 200) receives signals from pseudolites 520, 525and 530 that transmit GPS-like signals that may be utilized to determinethe position of the aircraft 515. The timing reference for thesepseudolites 520, 525 and 530 may be derived from the CDMA signalproduced by cellular base stations located nearby (not shown). Forexample, GPS receiver 525 may be modified to consider the ground basedpseudolites as satellites and different Gold (PN) codes may be assignedso that their transmissions would not interfere with the standard GPSsatellite signals. Thus, the CDMA signal in conjunction with thepseudolite signals may be used to determine the location of the aircraft515 (or other receiver).

In another embodiment of the present invention, and in reference to FIG.5, the location of a mobile position detection system maybe determinedusing an inverse multilateration method. As shown in FIG. 5, the methodof inverse multilateration may be accomplished in a system comprising aground-based transmitter 2605 that transmits a pulse at regularintervals, and a detector (e.g., a receiver mounted in an airborneplatform 2610 or the like). The ground-based transmitter 2605, transmitsa pulse at time t_(xmt in), and the pulse is received by the airborneplatform 2610 at time t_(in).

The subsequent pulse is transmitted by the ground-based transmittingsensor 2605 at time t_(xmt in+1), and the repetition time betweenadjacent pulses may be calculated by:t _(xmt in+1) −t _(xmt in=) Dport _(xmt in)=(in−1)Dp+t _(xmt 1.)

The slant range 2615 from the ground-based transmitting sensor to theairborne platform 2610 at each moment of signal interception maybecalculated by:Sr _(in) =C(t _(xmt in) −t _(in)),

-   -   where, in=1, . . . , Ns and,

C is the speed of light, or propagation speed.

If the position of the ground-based transmitter 2605 is represented by{right arrow over (P)}_(sensor)=[x_(sensor)y_(sensor)z_(sensor)]^(T),the slant range between the ground-based transmitter 2605 and theairborne platform 2610 at time t_(in) may be calculated bySr_(in)=∥{right arrow over (P)}_(planein)−{right arrow over(P)}_(sensorin)∥.

The position vector of the ground-based transmitting sensor may berepresented by {right arrow over(P)}_(senor)=[x_(sensor)y_(sensor)z_(sensor)]^(T) based on the time ofarrival of each pulse, the repetition time of the transmit pulse and theposition vector of the airborne platform 2610 which is represented by${\overset{\rightarrow}{P}}_{planein} = {\begin{bmatrix}x_{planein} \\y_{planein} \\z_{planein}\end{bmatrix}.}$The slant range between the transmitting ground-based sensor and anyairborne platform 2610 may also be calculated byC(t_(in)−t₁),

-   -   where t_(in) is the time a transmitted signal is intercepted by        an airborne platform 2610 in and to is the time a transmitted        signal is intercepted by an airborne platform 2610. Using the        notations described earlier, for in=1, . . . ,Ns:        c(t_(i  n) − t₁) = c(t_(in) − t_(xmt  in) + t_(xmt  in) − t₁)   = c(t_(in) − t_(xmt  in)) + c(t_(xmt  in) − t₁)   = c(t_(in) − t_(xmt  in)) + c((in − 1)Dp + t_(xmt  1) − t₁)   = c(t_(in) − t_(xmt  in)) − c(t₁ − t_(xmt  1)) + c(in − 1)Dp   = sr_(in) − sr₁ + c(in − 1)Dp.    -   and knowing that sr_(in)=∥{right arrow over        (P)}_(plane in)−{right arrow over (P)}_(sensor)∥. Combining the        two slant range expressions yields        c(t _(in) −t ₁)=∥{right arrow over (P)} _(plane in) −{right        arrow over (P)}sensor ∥−∥{right arrow over (P)} _(plane in)        −{right arrow over (P)} _(sensor) ∥+c(in−1)Dp,        or        ∥{right arrow over (P)} _(plane in) −{right arrow over (P)}        _(senor) ∥=c(t _(in) −t ₁−(in−1)Dp)+∥{right arrow over (P)}        _(plane 1) −{right arrow over (P)} _(sensor)∥.

Squaring both sides gives${{{\overset{\rightarrow}{P}}_{{plane}\quad{in}} - {\overset{\rightarrow}{P}}_{sensor}}}^{2} = \left( {{c\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)} + {{{\overset{\rightarrow}{P}}_{{plane}\quad 1} - {\overset{\rightarrow}{P}}_{sensor}}}} \right)^{2}$${{{\overset{\rightarrow}{P}}_{{plane}\quad{in}}}^{2} - {2\left\langle {{\overset{\rightarrow}{P}}_{{plane}\quad{in}},{\overset{\rightarrow}{P}}_{snesor}} \right\rangle} + {{\overset{\rightarrow}{P}}_{sensor}}^{2}} = {{c^{2}\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}^{2} - {2{c\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}{{{\overset{\rightarrow}{P}}_{{plane}\quad 1} - {\overset{\rightarrow}{P}}_{sensor}}}} + {{\overset{\rightarrow}{P}}_{{plane}\quad 1}}^{2} - {2\left\langle {{\overset{\rightarrow}{P}}_{{plane}\quad 1},{\overset{\rightarrow}{P}}_{sensor}} \right\rangle} + {{\overset{\rightarrow}{P}}_{sensor}}^{2\quad}}$${{{\overset{\rightarrow}{P}}_{{plane}\quad{in}}}^{2} - {2\left\langle {{\overset{\rightarrow}{P}}_{{plane}\quad{in}},{\overset{\rightarrow}{P}}_{sensor}} \right\rangle}} = {{c^{2}\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}^{2} - {2{c\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}{{{\overset{\rightarrow}{P}}_{{plane}\quad 1},{\overset{\rightarrow}{P}}_{sensor}}}} + {{\overset{\rightarrow}{P}}_{{plane}\quad 1}}^{2} - {2{\left\langle {{\overset{\rightarrow}{P}}_{{plane}\quad 1},{\overset{\rightarrow}{P}}_{sensor}} \right\rangle.}}}$

Reorganizing the equation gives${\left\langle {{2\left( {{\overset{\rightarrow}{P}}_{{plane}\quad{in}} - {\overset{\rightarrow}{P}}_{{plane}\quad 1}} \right)},{\overset{\rightarrow}{P}}_{sensor}} \right\rangle - {2{c\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}{{{\overset{\rightarrow}{P}}_{{plane}\quad 1} - {\overset{\rightarrow}{P}}_{sensor}}}}} = {{- {c^{2}\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}^{2}} + {{\overset{\rightarrow}{P}}_{{plane}\quad{in}}}^{2} - {{\overset{\rightarrow}{P}}_{{plane}\quad 1}}^{2}}$

-   -   defining a new variable s{overscore (r)}₁=∥{right arrow over        (P)}_(plane 1)−{right arrow over (P)}_(sensor)∥, which will        allow the equations for in=1, . . . , Ns to be recast as a        linear system of equations A₁{right arrow over (v)}=b₁, with the        unknown vector defined as:        ${\overset{\rightarrow}{v}}_{1} = {\begin{bmatrix}        x_{sensor} \\        y_{sensor} \\        z_{sensor} \\        {\overset{\sim}{sr}}_{1}        \end{bmatrix}\quad{and}}$ $A_{1} = \begin{bmatrix}        {{2x_{{plane}\quad 2}} - {2x_{{plane}\quad 1}}} & {{2y_{{plane}\quad 2}} - {2y_{{plane}\quad 1}}} & {{2z_{{plane}\quad 2}} - {2z_{{plane}\quad 1}}} & {{- 2}{c\left( {t_{2} - t_{1} - {Dp}} \right)}} \\        \vdots & \vdots & \vdots & \vdots \\        {{2x_{{plane}\quad{in}}} - {2x_{{plane}\quad 1}}} & {{2y_{{plane}\quad{in}}} - {2y_{{plane}\quad 1}}} & {{2z_{{plane}\quad{in}}} - {2z_{{plane}\quad 1}}} & {{- 2}{c\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}} \\        \vdots & \vdots & \vdots & \vdots \\        {{2x_{{plane}\quad{Ns}}} - {2x_{{plane}\quad 1}}} & {{2y_{{plane}\quad{Ns}}} - {2y_{{plane}\quad 1}}} & {{2z_{{plane}\quad{Ns}}} - {2z_{{plane}\quad 1}}} & {{- 2}{c\left( {t_{Ns} - t_{1} - {\left( {{Ns} - 1} \right){Dp}}} \right)}}        \end{bmatrix}$ $b_{1} = {\begin{bmatrix}        {{{\overset{\rightarrow}{P}}_{{plane}\quad 2}}^{2} - {{\overset{\rightarrow}{P}}_{{plane}\quad 1}}^{2} - {c^{2}\left( {t_{2} - t_{1} - {Dp}} \right)}^{2}} \\        \vdots \\        {{{\overset{\rightarrow}{P}}_{{plane}\quad{in}}}^{2} - {{\overset{\rightarrow}{P}}_{{plane}\quad 1}}^{2} - {c^{2}\left( {t_{in} - t_{1} - {\left( {{in} - 1} \right){Dp}}} \right)}^{2}} \\        \vdots \\        {{{\overset{\rightarrow}{P}}_{{plane}\quad{Ns}}}^{2} - {{\overset{\rightarrow}{P}}_{{plane}\quad 1}}^{2} - {c^{2}\left( {t_{Ns} - t_{1} - {\left( {{Ns} - 1} \right){Dp}}} \right)}^{2}}        \end{bmatrix}.}$

The method of least squares may be used to solve this linear system sothat {right arrow over (v)}₁=(A₁ ^(T)Q⁻¹A₁)⁻¹A₁ ^(T)·b₁ where Q is themeasurement covariance matrix nominally set as identity matrix ofdimension (Ns−1)×(Ns−1).

Methods of implementing an Inverse Multilateration computation inaccordance with embodiments of the invention can be summarized asfollows. As the mobile detection system (e.g., airplane 2610) movesalong a curve, the receiver onboard the mobile detection system collectsthe arrival times of the pulses from the ground-based transmittingsensor and the position of the detection system at each time of arrival.Then the position of the ground transmitter is computed by solving{right arrow over (v)}₁=(A ₁ ^(T)Q⁻¹A₁)⁻¹ A ₁ ^(T) Q ⁻¹ ·b ₁.

Of course, once the position of the ground transmitter is known, therelative position of the mobile detection system 2610 with respect tothe transmitter may also be computed.

In another embodiment, a Monte Carlo approach may be included in theinverse multilateration technique. For example, a Monte Carlo techniquemay be used in order to have an added Gaussian noise error added to thetime of arrival data,t _(in) =t _(—)0_(in) +N(σ_(t))

-   -   where, t_(—)0_(in) is the actual time of arrival of the        transmitted signal by the ground-based transmitter 2605 at the        airborne platform 2610, and N (σ_(t)) is random Gaussian noise        error of variance σ_(t).

A simulation of the inverse multilateration technique may be applied toa three dimensional case, wherein the ground-based transmitting sensoris positioned at${{\overset{\rightarrow}{P}}_{sensor} = {\begin{bmatrix}200 \\150 \\100\end{bmatrix}.}},$while the airborne platform 2610 may be defined by${{{\overset{\rightarrow}{P}}_{plane}(t)} = \begin{bmatrix}{R\quad{\cos\left( {\theta(t)} \right)}} \\{R\quad{\sin\left( {\theta(t)} \right)}} \\{{alt}(t)}\end{bmatrix}},$where alt(t)=alt₀+D_(alt) sin(2#f_(aft)t) and θ(t)=θ₀+Δθ.t. In thissimulation, the airborne platform 2610 may be presumed to move in acircular, sinusoidal path and thereby maintaining reasonable diversityin all three axial directions, where R=500 m, alt₀=500 m, D_(alt)=200 m,f_(alt)= 1/60 seconds, θ₀=0 degrees, Λθ=400 Knots/R, Dp=4 seconds, andthe variance of the added Gaussian errors to the time of arrival data isσ_(t) ²=(0 m/c)² for case one, (5 m/c)² for case two and (30 m/c)² forcase three. The added Gaussian errors to the airborne platform 610position may have the variance σ_(x) ²=σ_(y) ²=σ_(z) ² which is equal to(0 m)² for case 1, (5 m)² for case two and (10 m)² for case three.

The invention now being fully described, it will be apparent to one ofordinary skill in the art that many changes and modifications can bemade thereto without departing from the spirit or scope of the inventionas set forth herein. The foregoing describes some embodiments of theinvention along with a number of possible alternatives. Theseembodiments, however, are merely for example and the invention is notrestricted thereto. It will be recognized that various materials andmodifications may be employed without departing from the inventiondescribed above, the scope of which is set forth in the followingclaims.

1. A method for locating an object utilizing inverse multilateration,the method comprising: receiving signal pulses from a transmittingobject at a mobile detection device; calculating a slant range betweenthe transmitting object and the mobile detection device; calculating aposition vector of the transmitting object based at least in part on theslant range.
 2. The method of claim 1 wherein the calculation of theposition vector of the transmitting object further comprises computing{right arrow over (v)}₁=(A₁ ^(T)Q⁻¹A₁)⁻¹A₁ ^(T)Q⁻¹·b₁.
 3. The method ofclaim 1 wherein the calculation of a slant range further comprises useof time of arrival data.
 4. The method of claim 3 wherein a knowndistribution of noise is added to the time of arrival data.
 5. Themethod of claim 1 wherein receiving signals pulses from a transmittingobject further comprises computing the repetition time between adjacentpulses.
 6. The method of claim 1 wherein the signal pulses aretransmitted from a fixed object and the mobile detection device isairborne.
 7. A system for locating an object utilizing inversemultilateration, the method comprising: a receiver for receiving signalpulses from a transmitting object at a mobile detection device; acalculator for calculating a slant range between the transmitting objectand the mobile detection device; and a position vector calculator forcalculating a position vector of the transmitting object based at leastin part on the slant range.